.hdr versus .jpg environment maps
You can't.

To understand why, it would require dissecting a typical JPEG transfer curve.

The TL;DR is that a typical display referred photograph encoded to sRGB can only encode approximately two and a bit stops over middle grey, where middle grey is mapped to 0.18. 0.18+0.18 is one stop to 0.36, 0.36+0.36 is two stops to 0.72, and 0.72+0.72 is 1.44 for three stops, which the display linear linearization maxes out at 1.0.

Any particular photograph represents well over this dynamic range of course. As a result, the method the camera or software uses to encode the additional stops back into the scene is using a unique and custom transfer curve. Once in the display referred encoded domain however, that original transfer characteristic is lost and unrecoverable.

You can guess, estimate, etc., but it will never be even remotely accurate due to the number of stops compressed into the image and the limited dynamic range of an sRGB transfer curve.

Scene referred imagery is vastly different than display referred, and as such, it is very much a one-way street in terms of data flows.

In addition to this, .HDR is a less reliable storage format for scene referred imagery as compared to .EXR. Avoid it when possible.